FastDFL: Reusable local QP solution maps for decision-focused learning

Decision-focused learning (DFL) trains predictors through downstream optimization problems, but repeatedly solving the downstream problem and differentiating its solution make training expensive. We study DFL for strongly convex quadratic programs (QPs) with a fixed Hessian and feasible set, where predictions enter the linear term of the objective. During training, evolving predictions can revisit regions where the optimal decision is affine in the prediction and its Jacobian is constant. We propose FastDFL to turn this recurrence into reusable computation. FastDFL constructs a local formula only after the same constraint structure is observed twice, verifies its validity before reuse, and limits the cost of retrieving previously useful formulas. Whenever a formula passes the Karush-Kuhn-Tucker (KKT) validity checks, it returns the same decision and Jacobian as a fresh QP solve and differentiation. Across three benchmarks and two predictor architectures, FastDFL replaces more than half of the QP solves and derivative computations in every setting. It makes end-to-end training 1.35 to 3.47 times as fast as an otherwise identical procedure that solves each QP and differentiates its solution, while leaving decision quality nearly unchanged.